How to solve this trig equation in radians 2sin^2(x) + sin(x) - 1=0

[UrbanXrisis]

I just got a review sheet in math that contain questions that I don't know how to do from last year. ONe asks to solve for all values of theta of [0,2pi] in radians: 2sin^2(theta)+sin(theta)-1=0

any ideas?

 

[Leong]

Use
$$sin\ 2\theta = 2\ sin\ \theta\ cos\ \theta$$
$$sin^2\ \theta + cos^2\ \theta = 1$$

 

[UrbanXrisis]

that confuses me more. I have no clue what the question is even asking, I think I forgot all my math. Could you give a longer explanation?

 

[recon]

Let $$sin\ \theta\ = x$$

Then your original equation now looks like $$2x^2 + x - 1 = 0$$.

Solve the quadratic equation. Once you do that, the rest should be easy.

 

[Pyrrhus]

that confuses me more. I have no clue what the question is even asking, I think I forgot all my math. Could you give a longer explanation?

The question is asking for which angles in a 0 to 2pi interval satisfy that equation.

-Cyclovenom

 

[Leong]

forget about what i have said. use recon's suggestion and understand cyclovenom's point.